cf578c Weakness and Poorness 三分

给定一个长度为n的数组ai，求一个实数x，使得序列a1-x,a2-x,...,an-x的不美好程度最小。

不美好程度定义为，一个序列的所有连续子序列的糟糕程度的最大值。

糟糕程度定义为，一个序列的所有位置的和的绝对值。

输入 第一行n。

第二行n个数，表示ai。

输出 一个实数，精确到6位小数，表示最小不美好程度值。

#include<iostream>
#include<cstdio>
#include<cmath>
#include<ctime>
#include<queue>
#include<algorithm>
#include<cstring>
using namespace std;
#define duke(i,a,n) for(int i = a;i <= n;i++)
#define lv(i,a,n) for(int i = a;i >= n;i--)
#define clean(a) memset(a,0,sizeof(a))
const int INF = 1 << 30;
typedef long long ll;
typedef double db;
template <class T>
void read(T &x)
{
    char c;
    bool op = 0;
    while(c = getchar(), c < ‘0‘ || c > ‘9‘)
        if(c == ‘-‘) op = 1;
    x = c - ‘0‘;
    while(c = getchar(), c >= ‘0‘ && c <= ‘9‘)
        x = x * 10 + c - ‘0‘;
    if(op) x = -x;
}
template <class T>
void write(T x)
{
    if(x < 0) putchar(‘-‘), x = -x;
    if(x >= 10) write(x / 10);
    putchar(‘0‘ + x % 10);
}
const int maxn = 2e5 + 5;
const db eps = 1e-8;
int arr[maxn];
db arr1[maxn];
int n;
db calc(db arr[])
{
    db t = 0;
    db res = arr[0];
    duke(i,0,n - 1)
    {
        t = arr[i] + t;
        res = max(res,t);
        if(t < eps)
        t = 0;
    }
    return res;
}
db solve(db t)
{
    duke(i,0,n - 1)
    {
        arr1[i] = arr[i] - t;
    }
    db x1 = calc(arr1);
    duke(i,0,n - 1)
    arr1[i] = -arr1[i];
    db x2 = calc(arr1);
    db x = max(fabs(x1),fabs(x2));
    return x;
}
int main()
{
    read(n);
    int maxnum = -10001,minnum = 10001;
    duke(i,0,n - 1)
    {
        read(arr[i]);
        maxnum = max(maxnum,arr[i]);
        minnum = min(minnum,arr[i]);
    }
    int dcnt = 100;
    db l = minnum ,r = maxnum;
    while(dcnt--)
    {
        db m1 = l + (r - l) / 3;
        db m2 = r - (r - l) / 3;
        db x1 = solve(m1);
        db x2 = solve(m2);
        if(x1 > x2)
        {
            l = m1;
        }
        else
        {
            r = m2;
        }
    }
    db res = solve(l);
    printf("%.8lf\n",res);
    return 0;
}